Energy of Wave

Q. Which of the following phenomena is due to propagation of a wave?

1. Vibration of a window panel when a supersonic aircraft passes
2. Breaking of glasses by opera singers by singing
3. Transportation of particles of a medium when a wave passes
4. Both (a) and (c)

Q. A harmonic wave propagates in a medium. Find the average energy density of the wave, if at any point, the energy density becomes equal to $W_0$ at an instant $t=t_0+T/6$, where $t_0$ is the instant when amplitude is maximum at this location and $T$ is the time period of oscillation.

1. $\frac{3}{2}{W}_0$
2. $2W_0$
3. $\frac{2W_0}{3}$
4. $\frac{W_0}{2}$

Q. A taut string for which $\mu =15\times {10}^{-2}\text{kg/m}$ is under a tension of $240\text{N}$. How much power must be supplied to the string to generate sinusoidal waves at a frequency of $18.0\text{Hz}$ and an amplitude of $18\text{cm}$?

1. $1300\text{W}$
2. $1240\text{W}$
3. $1280\text{W}$
4. $1220\text{W}$

Q. A sinusoidal wave on a string is described by the wave function
$y=0.3\sin (1.6x-100t)$
where $x$ and $y$ are in $\text{metre}$ and $t$ is in $\text{second}$. The mass per unit length of this string is $10\text{g/m}.$ Determine the power transmitted to the wave.

1. $260\text{J}$
2. $281\text{J}$
3. $360\text{J}$
4. $320\text{J}$

Q. A $400\text{Hz}$ wave with amplitude $2\text{mm}$ travels on a long string of linear mass density $5\text{g/m}$ kept under a tension of $50\text{N}$. Find the average power and total energy associated with the wave in a $2\text{m}$ long portion of the string.

1. $1\text{W}$ , $6\text{J}$
2. $6.32\text{W}$ , $0.13\text{J}$
3. $6\text{W}$ , $1\text{J}$
4. None of the above

Q. A sinusoidal transverse wave travels on a string of length $4\text{m}$ and mass $4\text{g}$. The wave speed is $20\text{m/s}$ and the wavelength is $0.2\text{m}$. If the wave is to have an average power of $50\text{W}$, then

1. tension induced in the string is $0.4\text{N}$.
2. frequency of wave will be $100\text{Hz}$.
3. linear mass density of the given string must be ${10}^{-3}\text{kg/m}$.
4. amplitude of the wave will be $11.25\text{cm}$

Q. Statement (A): In a small segment of string carrying a sinusoidal wave, the total energy is conserved.

Statement (B) : Every small part of the string performs SHM and in SHM, the total energy is conserved .

1. Both (A) and (B) are correct
2. None of these
3. (A) is correct only
4. (B) is correct only

Q. A transverse wave of amplitude $0.5\text{mm}$ and frequency $100\text{Hz}$ is produced on a wire stretched to a tension of $100\text{N}$. If the wave speed is $100\text{m/s}$. What average power is the source transmitting to the wire?

1. $60\text{mJ/s}$
2. $49\text{mJ/s}$
3. $40\text{mJ/s}$
4. $70\text{mJ/s}$

Q. A sinusoidal transverse wave travels on a string of length $4\text{m}$ and mass $4\text{g}$. The wave speed is $20\text{m/s}$ and the wavelength is $0.2\text{m}$. If the wave is to have an average power of $50\text{W}$, then

1. tension induced in the string is $0.4\text{N}$.
2. frequency of wave will be $100\text{Hz}$.
3. linear mass density of the given string must be ${10}^{-3}\text{kg/m}$.
4. amplitude of the wave will be $11.25\text{cm}$

Q. Which of the following phenomena is due to propagation of a wave?

1. Vibration of a window panel when a supersonic aircraft passes
2. Transportation of particles of a medium when a wave passes
3. Breaking of glasses by opera singers by singing
4. Both (a) and (c)